Can we make our fluid domain object from a cylinder?
Yes, you can use Cylinder object as domain, but shape is not used in calculation, only dimension of the object (see Xylvier's answer). 

So just an extension ... if you need liquid inside cylindrical shape
- use Cylinder object as Effector (Physics Properties > Liquid).

Common problem is blocky colision (outer) shape.
You can solve it by using Boolean modifier > Intersect > Object - the same cylinder object.